1. Field of the Invention
This invention relates to induction motor control systems, and, more particularly, to systems for automatically controlling the power factor and corresponding efficiency of an induction motor that is subjected to varying mechanical loads.
2. Description of the Prior Art
Neglecting wire resistance and friction and other second-order effects, a useful first-order electric model of an induction motor is depicted in FIG. 1(a), wherein R represents the electrical power dissipating element of the motor (i.e., the element that absorbs the power that is converted by the motor into mechanical power) and L.sub.m represents the effective collective inductance of the motor's windings. This model, converted into the "frequency domain" as per Steinmetz, becomes the conductance G (i.e., 1/R.sub.m) in parallel with the susceptance B.sub.m (i.e., l/j.omega.L.sub.m or -j/.omega.L.sub.m) as shown in FIG. 1(b). In the complex plane G and B.sub.m add vectorially to yield the overall admittance Y of the motor model (i.e., Y=G-j/.omega.L.sub.m) as depicted in FIG. 2(a). At full rated mechanical load for the motor the corresponding model value of G is at its highest acceptable magnitude G.sub.m as shown in FIG. 2(b) (corresponding to the lowest acceptable magnitude of R which dissipates the maximum allowable electrical power for the motor as rated). The minimum phase lag angle, .theta..sub.m (i.e., Arctan 1/G.sub.m .omega.L.sub.m), defines the steady state phase lag of the fully-loaded motor's substantially sinusoidal current with respect to the applied sinusoidal line voltage V.sub.s, i.e., EQU I.sub.m =.vertline.V.sub.s .vertline.(.sqroot.G.sup.2.sub.m +.vertline.B.sub.m .vertline..sup.2) .theta..sub.m.
Generally the load current I of an induction motor lags the applied voltage V.sub.s by .theta. radians as depicted in FIGS. 3(a) and 3(b), wherein EQU I=V.sub.s .multidot.Y=V.sub.s (G-j.vertline.B.vertline.),
or EQU I=(V.sub.s)(G)-j(V.sub.s)(.vertline.B.vertline.)=I.sub.G -jI.sub.B.
FIG. 4 differs from FIG. 3(b) only in that each current vector has been multiplied by the applied voltage vector to yield the "power" diagram wherein: EQU Watts=.vertline.V.sub.s .vertline..sup.2 G=.vertline.V.sub.s .vertline..multidot..vertline.I.sub.G .vertline.; EQU V.A.R.=Volt-Amperes-Reactive=.vertline.V.sub.s .vertline..sup.2 .multidot..vertline.B.vertline.=.vertline.V.sub.s .vertline..multidot..vertline.I.sub.B .vertline.; EQU V.A.=Volt-Amperes=.vertline.V.sub.s .vertline..sup.2 .multidot..vertline.Y.vertline.=.vertline.V.sub.s .vertline..multidot..vertline.I.vertline.;
and EQU V.A.=WATTS-jV.A.R.
The Power Factor ("P.S.") is a measure of the relationship between the magnitude of V.A. and the magnitude of Watts and is defined as EQU P.F.=cos .theta.=cos [(Arctan(.vertline.I.sub.B .vertline./.vertline.I.sub.G .vertline.)
or, EQU P.F.=cos [Arctan(.vertline.V.A.R..vertline./.vertline.Watts)]
The phase lag, whether expressed in radians or as a power factor, corresponds to a "real time" lag of .DELTA.t=.THETA./.omega. wherein .omega. is the angular frequency of the applied voltage. So, the input voltage and current to this simplified model of an uncompensated induction motor are both substantially sinusoidal, but out of phase as shown in FIG. 5. An induction motor has a continuously variable amount of phase shift which varies inversely with the mechanical load (i.e., torque) applied on the motor's rotating shaft. In other words, a fully-loaded induction motor has only a small phase shift (i.e., a high power factor), whereas a lightly-loaded induction motor will display a relatively large phase shift (as depicted in FIG. 2(a) wherein G&lt;G.sub.m but B.sub.m remains substantially constant so that .theta.&gt;.theta..sub.m) i.e., a lowered power factor. A reduced power factor implies an undesirably high amount of current flowing into the motor for the corresponding amount of mechanical power produced. When the motor is under-loaded, G becomes lower than G.sub.m, whereas B.sub.m remains substantially constant. Hence the lag angle .theta. increases and the motor's Power Factor (P.F.) decreases. FIG. 6 depicts this relationship. Note that when G&gt;G.sub.m, an overload condition exists and when .theta. reaches .theta..sub.s the motor will stall. For industrial loads, a low power factor condition is a significant problem for the power company supplying the electricity. This is due to the fact that the power company loses a significant amount of power along its transmission lines in so-called "I.sup.2 R" losses. These losses obviously increase at an increasing rate as the current supplied increases. It is therefore necessary for power companies to charge a premium price for power supplied at a low power factor.
To avoid this waste of energy and loss of revenues, industrial users routinely employ means to "correct" (i.e., raise) the power factors of their loads. The classical approach is to connect a bank of capacitors across the industrial plant's input power lines. There are two major problems with this approach: (1) the correction is a fixed one, so that if the industrial load varies (as they all do) the correction becomes either less effective or, conversely, potentially overly effective, resulting in an undesirably low leading power factor; and, (2) many industrial capacitor banks have inherently unpredictable maintenance problems.
It would therefore be highly desirable to have a system that would automatically correct the power factor of an induction motor in real time (i.e., "on the fly"), so that the motor runs at or near optimum efficiency continuously as the applied mechanical load is varied.
In order to accomplish this it is useful to note that the "full-load" condition of an induction motor is directly proportional to the line voltage applied to the motor; i.e., if an induction motor is underloaded at a given line voltage, then one way to get the motor back to a "fully-loaded" condition is to reduce the effective voltage applied to the motor by phase control of the applied voltage. This well-known technique is typically implemented with Triacs or SCR groups that are put in series with the motor across the supply line voltage. These devices are triggered part way through the supply line voltage cycle (typically when the motor current reaches the zero level) so that the voltage applied to the motor is reduced, not in peak value, but in average value due to the change in waveshape as depicted in FIGS. 7(a) and 7(b). The control signal determining the off-time for the Triacs or SCRs is an analog voltage signal that is synchronized with the supply line voltage and is made directly or indirectly proportional to a controlling quantity that is different for different systems.
By reducing the effective applied voltage such that the motor's new electrical load condition nearly matches its actual applied mechanical load, the electrical motor losses are significantly reduced and the overall efficiency of the motor is improved.
Various approaches have been employed in the prior art to accomplish some control of induction motors to improve their efficiency.
U.S. Pat. No. 4,388,578 discloses an example of a power factor controller for an induction motor which produces a signal proportionate to the magnitude of the motor's load phase angle (measured by "zero crossings" of line voltage and line current) and uses that signal to adjust the power supplied to the motor.
U.S. Pat. No. 4,242,625 discloses an induction motor controller that makes use of the "slip speed" of the motor to control its applied voltage. Since slip speed is directly related to the applied mechanical load, it is used as a measure of the mechanical loading, and the phase angle controlled voltage to the motor is automatically adjusted accordingly to attempt to maintain a substantially constant slip speed.
U.S. Pat. No. 4,636,702 discloses an induction motor controller that attempts to measure the presumed sinusoidal peak line current value by measuring the slope (i.e., time rate of change) of the line current near the current "zero crossing." The peak current level signal thus deduced is then used as an indication of the percent loading (as compared to full loading) of the motor, and serves as a control signal to determine the appropriate phase angle controlled voltage to be applied to the motor.
These approaches described above are somewhat useful in special applications, but all are limited in effectiveness by problems such as over-compensation with the concurrent potential for motor stalling, lack of sensitivity of control, or failure to recognize non-sinusoidal current waveforms.
It is therefore an object of this invention to provide an improved approach for induction motor efficiency enhancement that is less likely to result in possible motor stalling.
It is another object of this invention to provide an improved approach for induction motor efficiency enhancement that is highly sensitive to "underloading".
It is yet another object of the instant invention to provide an improved approach for induction motor efficiency enhancement that works well notwithstanding the non-sinusoidal current waveforms associated with many industrial induction motors.